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nathanielbd/machine_problem_3.ipynb

Created April 26, 2021 21:15
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machine_problem_3.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "pediatric-activation",
"metadata": {},
"source": [
"# Machine Problem 3\n",
"### Nathaniel Budijono\n",
"#### April 26, 2021\n",
"\n",
"Define the function $f(x)$ which returns 1 if the input is 2 and 0 otherwise. Pass this function to the $U_f$ function, which will create the matrix for the corresponding oracle. Set the number of input qubits, $n=2$ and number of workspace qubits, $m=1$. Use the function `GroverDiffusion` to get the matrix for $G$, the diffusion operator. Pass a quantum state through the circuit. Apply 6 iterations of the oracle and diffusion operator. After each iteration, use the `plotprobs` function to show the measurement probabilities of the quantum state. Explain the results."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "fallen-chorus",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n",
"Attaching package: ‘QuantumOps’\n",
"\n",
"\n",
"The following object is masked from ‘package:stats’:\n",
"\n",
" dist\n",
"\n",
"\n",
"The following objects are masked from ‘package:base’:\n",
"\n",
" I, norm, single\n",
"\n",
"\n"
]
}
],
"source": [
"library('QuantumOps')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "proof-conducting",
"metadata": {},
"outputs": [],
"source": [
"f <- function(x){\n",
" if (x == 2) {\n",
" 1\n",
" }\n",
" else {\n",
" 0\n",
" }\n",
"}\n",
"O <- Uf(f, 2, 1)\n",
"G <- GroverDiffusion(2)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "corresponding-davis",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"dataframe\">\n",
"<caption>A matrix: 8 × 1 of type cpl</caption>\n",
"<tbody>\n",
"\t<tr><td> 0.3535534+0i</td></tr>\n",
"\t<tr><td>-0.3535534+0i</td></tr>\n",
"\t<tr><td> 0.3535534+0i</td></tr>\n",
"\t<tr><td>-0.3535534+0i</td></tr>\n",
"\t<tr><td> 0.3535534+0i</td></tr>\n",
"\t<tr><td>-0.3535534+0i</td></tr>\n",
"\t<tr><td> 0.3535534+0i</td></tr>\n",
"\t<tr><td>-0.3535534+0i</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"A matrix: 8 × 1 of type cpl\n",
"\\begin{tabular}{l}\n",
"\t 0.3535534+0i\\\\\n",
"\t -0.3535534+0i\\\\\n",
"\t 0.3535534+0i\\\\\n",
"\t -0.3535534+0i\\\\\n",
"\t 0.3535534+0i\\\\\n",
"\t -0.3535534+0i\\\\\n",
"\t 0.3535534+0i\\\\\n",
"\t -0.3535534+0i\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A matrix: 8 × 1 of type cpl\n",
"\n",
"| 0.3535534+0i |\n",
"| -0.3535534+0i |\n",
"| 0.3535534+0i |\n",
"| -0.3535534+0i |\n",
"| 0.3535534+0i |\n",
"| -0.3535534+0i |\n",
"| 0.3535534+0i |\n",
"| -0.3535534+0i |\n",
"\n"
],
"text/plain": [
" [,1] \n",
"[1,] 0.3535534+0i\n",
"[2,] -0.3535534+0i\n",
"[3,] 0.3535534+0i\n",
"[4,] -0.3535534+0i\n",
"[5,] 0.3535534+0i\n",
"[6,] -0.3535534+0i\n",
"[7,] 0.3535534+0i\n",
"[8,] -0.3535534+0i"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"input <- tensor(intket(0, 2), ket(0, 1))\n",
"psi <- tensor(H(), H(), H()) %*% input\n",
"psi"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "demanding-species",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 1\n",
"[1] \"0.354|000> + -0.354|001> + 0.354|010> + -0.354|011> + -0.354|100> + 0.354|101> + 0.354|110> + -0.354|111>\"\n",
"[1] \"0.707|100> + -0.707|101>\"\n",
"[1] 2\n",
"[1] \"-0.707|100> + 0.707|101>\"\n",
"[1] \"-0.354|000> + 0.354|001> + -0.354|010> + 0.354|011> + 0.354|100> + -0.354|101> + -0.354|110> + 0.354|111>\"\n"
]
},
{
"data": {
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Drm3btitXrizzUytXrjzQ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\nTkSuQmCC",
"text/plain": [
"Plot with title “Absolute Value of Amplitudes”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 3\n",
"[1] \"-0.354|000> + 0.354|001> + -0.354|010> + 0.354|011> + -0.354|100> + 0.354|101> + -0.354|110> + 0.354|111>\"\n",
"[1] \"-0.354|000> + 0.354|001> + -0.354|010> + 0.354|011> + -0.354|100> + 0.354|101> + -0.354|110> + 0.354|111>\"\n"
]
},
{
"data": {
"image/png": 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MiRUpY5dOhQmRMDAKh2yQu7WCwWRdHJDqEdO3as9NW/+OKLyZMn//u///uJEyf+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\nYHdzcAAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Absolute Value of Amplitudes”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 4\n",
"[1] \"-0.354|000> + 0.354|001> + -0.354|010> + 0.354|011> + 0.354|100> + -0.354|101> + -0.354|110> + 0.354|111>\"\n",
"[1] \"2.78e-17|000> + -2.78e-17|001> + 2.78e-17|010> + -2.78e-17|011> + -0.707|100> + 0.707|101> + -2.78e-17|110> + 2.78e-17|111>\"\n"
]
},
{
"data": {
"image/png": 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MiRUpY5dOhQmRMDAKh2yQu7WCwWRdHJDqEdO3as9NW/+OKLyZMn//u///uJEyf+\n7d/+7Z577jn9bUZR1KxZs+eff770ZVatWvVf//VfZW4KAKB6JS/sWrZsmZqaGv9gXGH79+9P\nTU1t1apVKeu+/vrro0aN2rlz56BBg/7lX/7loosuOv1tAgAEJnknT9SqVatly5bbt28vMr5z\n5842bdrUqnXSmTz22GNDhw6tV69e/Momiao7nW0CAIQnqenTq1evnJyc7OzsxMjGjRu3bduW\nmZl5slWef/75n/70p8OGDVu7dm2J16WrwDYBAIKU1LAbOXJkFEUTJkxIjEycODGKolGjRsV/\nzM/P37dv38GDB+M/xmKxSZMmNWrUaMaMGY0bN67YNgEAviaS+s0Tffv2HThw4MyZM3fs2NG9\ne/eVK1cuXbo0KysrcShu+fLl/fv379Kly9q1a6Mo+uSTTzZv3ty8efMRI0YU39pLL73UokWL\nMrcJAPA1kdSwS0lJee211yZPnrxo0aIpU6ZcdNFF48aNe+SRR062fE5OThRF+/bte+utt4rf\nm5eXV4FtAgCEKqlhF0VRvXr1xo4dO3bs2BLvvfbaa+NXMInr169f4R8rtk0AgK8J540CAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAE9VA2gAACAA\nSURBVARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBCLZYZeXlzdhwoTMzMwmTZpkZmaOHz8+Ly+vnOs+88wzTZs2LT6ekZGRUszjjz9eqRMHAKjp\n0pL8+2688cb58+d36tRp2LBhq1evHjNmzOrVqxcsWFDmiocPH3766aeLjx85cmTHjh3p6ekd\nO3YsPN6uXbtKmzQAwFdBUsNu6dKl8+fPz8rKmjt3bmpq6vHjxwcPHrxw4cJly5b17t37ZGv9\n8Y9/XLdu3YwZMzZt2nTmmWcWuTc7OzsWi40aNeqxxx6r4ukDANRoSQ27qVOnRlE0efLk1NTU\nKIrS0tImTZq0aNGi6dOnlxJ2Q4cOPXr06Mnu3bp1axRFnTp1qoL5AgB8lSQ17JYtW5aRkXHx\nxRcnRrp27Zqenr5kyZJS1jp48GD8xuWXX75z584i98bD7rzzzps1a9bWrVvPPvvsHj16FP4V\nAABfE8kLu4KCgj179vTo0aPIeEZGxpo1a2KxWEpKSokr1q1bN36jVq0STvWIh11WVtbevXvj\nIykpKSNHjnzqqadq165dabMHAKjxkndW7N69e0+cONGsWbMi482bN8/Pz9+/f3/FNrtly5Yo\ninr37r1+/fovvvhixYoVV1555bPPPvvzn/+8PKvn5OTUrVu3+Em1hWVmZkZRFIvFKjZDAIDk\nSN4Ru3gYneyw3LFjxyq22dGjR+fn5w8cODC+5Z49ey5YsKBjx46TJk368Y9/XOJBvsLatWv3\n1ltvlX7Jlffff/+BBx442cwBAGqI5IVdy5YtU1NTDxw4UGR8//79qamprVq1qthm+/fvX2Sk\nRYsW/fr1mz17dnZ2dpFroBSXkpLSq1ev0pc544wzKjY3AIBkSt5bsbVq1WrZsuX27duLjO/c\nubNNmzZlHlo7JS1atIii6Pjx45W4TQCAGi6p3zzRq1evnJyc7OzsxMjGjRu3bdsW/xBbBWRn\nZ7dp0+b+++8vMr5hw4Y6deqUebgOACAkSQ27kSNHRlE0YcKExMjEiROjKBo1alT8x/z8/H37\n9iWub1KmCy644Kyzzpo2bdrq1asTgy+88MKqVatuvfXWtLRkf68GAEA1Smr69O3bd+DAgTNn\nztyxY0f37t1Xrly5dOnSrKysxNWJly9f3r9//y5duqxdu7ac25w2bVqfPn169ep1/fXXt27d\n+q9//euKFSs6duz45JNPVtnjAACoiZJ6xC4lJeW1114bM2ZMbm7ulClTjh49Om7cuNmzZ5/O\nNrt167Zq1aohQ4a88847zz//fG5u7k9+8pN169Y1bdq0sqYNAPCVkOw3K+vVqzd27NixY8eW\neO+1115byuXiNmzYUOJ4165dT7MOAQACkNQjdgAAVB1hBwAQCGEHABAIYQcAEAhhBwAQCGEH\nABAIYQcAEAhhBwAQCGEHABAIYQcAEIiyw+7555//4osvkjAVAABOR9lhd+edd7Zq1erGG2/8\n/e9/f+TIkSTMCQCACig77H75y19269Ztzpw5N998c8uWLW+//fb58+fn5+cnYXIAAJRf2WH3\nv//3/166dOmOHTuefvrpK6644sUXXxw8eHDr1q3vvffeJUuWFBQUJGGWAACUqbwnT7Ru3frb\n3/52ovAuvvjiX//61/369TvnnHMeeOCBv/zlL1U6SwAAynTKZ8W2bt26Z8+e/fr1O++886Io\n2rVr13/8x3907969U6dOr7/+ehXMEACAckkr53LHjx9fsWLF3Llz58yZ88knn0RR1Lp165Ej\nR95www1nnXXWrFmzfvWrXw0bNmzx4sV9+/atygkDAFCyssNu9uzZc+fOnTdv3oEDB6Ioat++\n/Q9+8IMbbrihR48eKSkp8WW6du166623Xn755a+++qqwAwCoFmWH3U033RRF0aWXXvq9731v\n+PDhl156aYmLtW/fvkWLFu3atavkCQIAUD5lh92//uu/Dh8+/Pzzzy99scaNG+/du7eSZgUA\nwCkrO+zuvPPOhg0blnjX4cOH8/LymjZtWtmzAgDglJV9VmyLFi1efvnlEu968sknO3ToUNlT\nAgCgIk56xG7WrFmJ26tWrUpLK7rksWPH5s6de/jw4aqaGgAAp+KkYXfbbbclbk+dOnXq1Kkl\nLjZkyJDKnxQAAKfupGE3Z86c+I1hw4bdf//9/fr1K75M/fr1e/fuXVVTAwDgVJw07IYOHRq/\n0b9//6ysrAEDBiRrSgAAVMRJw27x4sVRFPXq1St+6C43N/dkSzZo0KAqZgYAwCk5adj1798/\niqLdu3e3bt269E3EYrFKnhQAAKfupGHXpUuXKIrS0tL++Z//OYnzAQCggk4admvXro3fmDZt\nWrImAwBAxZUcdidOnCj/JlJTUytpMgAAVFzJYVf8csSl8Bk7AICaoOSAK3x1YgAAvhJKDrsX\nXnghyfMAAOA0lX0du/z8/NI34Tp2AAA1gevYAQAEwnXsAAAC4Tp2AACBKO9lTWKx2HvvvZed\nnb1nz562bdt27ty5Xbt2VTozAABOSbnCbtmyZQ8++OCaNWsKD15//fVPPPFE586dq2ZiAACc\nmrLD7v333x80aNDhw4cHDx48cODA9PT0HTt2LFiw4I033nj77bfXrFmTnp6ehIkCAFC6ssPu\n0UcfPXLkyIsvvnjLLbckBr/zne/MmjXrtttu+9GPfjRz5syqnCEAAOVSq8wl3nnnnW9+85uF\nqy7u1ltv7dOnz8qVK6tmYgAAnJqywy4lJeX8888v8a7zzz8/Nze3sqcEAEBFlB1211xzzerV\nq4t//0ReXt7y5ct79uxZNRMDAODUlB12o0eP3r179y233PLJJ58kBnNycm666abt27f/8Ic/\nrMrpAQBQXiWfPPF3f/d3hX8866yzZs+ePWfOnHbt2rVu3XrXrl0fffRRQUHBNddcs3bt2m7d\nuiVlqgAAlKbksFu3bl2RkRYtWkRRdPDgwYMHD0ZR1KxZsyiKtmzZsmLFivvuu6+KJwkAQNlK\nDru9e/cmeR4AAJymsj9jV4qpU6eOGzeusqYCAMDpKNdXiu3atWvx4sX79u0rPJiXl/fUU0+d\nd955Y8aMqZq5AQBwCsoOu/Xr1/fr12///v3F76pdu/akSZOqYFYAAJyyst+KnTBhwueffz5l\nypRFixZ17tx5wIABq1evfvXVV6+88so+ffrcfvvtSZglAABlKjvsVq9efcUVV3znO98ZMGDA\n3Xff/d///d/dunW78cYbFy9evGbNmt/85jdJmCUAAGUqO+z27t17+eWXx29fc801mzZt+vzz\nz6Moaty48c033/zb3/62aicIAED5lB12Z511VuLqJ5dddllKSsrixYvjPzZv3nzNmjVVODsA\nAMqt7LDr1q3bvHnz5s2bV1BQ0KBBgw4dOsyePTt+15///OdGjRpV8QwBACiXssPu8ccfr1ev\n3vXXXz9jxowoigYMGPDiiy8OHTo0Kytr8eLFAwcOrPpJAgBQtrIvd9KlS5d33nnnhRdeaNeu\nXRRF48eP/+ijjxYuXJifn9+3b9+f/exnVT9JAADKVq4LFHfo0GH8+PHx22eeeeYbb7xx6NCh\nY8eONW/evCrnBgDAKShX2EVRFIvF3nvvvezs7D179rRt27Zz587xA3gAANQQ5Qq7ZcuWPfjg\ng0VOgL3++uufeOKJzp07V83EAAA4NWWH3fvvvz9o0KDDhw8PHjx44MCB6enpO3bsWLBgwRtv\nvPH222+vWbMmPT09CRMFAKB0ZYfdo48+euTIkRdffPGWW25JDH7nO9+ZNWvWbbfd9qMf/Wjm\nzJlVOUMAAMql7MudvPPOO9/85jcLV13crbfe2qdPn5UrV1bNxAAAODVlh11KSsr5559f4l3n\nn39+bm5uZU8JAICKKDvsrrnmmtWrV+fn5xcZz8vLW758ec+ePatmYgAAnJqyw2706NG7d+++\n5ZZbPvnkk8RgTk7OTTfdtH379h/+8IdVOT0AAMqr5JMn/u7v/q7wj2edddbs2bPnzJnTrl27\n1q1b79q166OPPiooKLjmmmvWrl3brVu3pEwVAIDSlBx269atKzLSokWLKIoOHjx48ODBKIqa\nNWsWRdGWLVtWrFhx3333VfEkAQAoW8lht3fv3iTPAwCA01T2Z+wKy83N3bJlyxdffFFFswEA\noMLKFXaHDh0aN25cenp6w4YNL7zwwiZNmrRp02bMmDFffvllVc8PAIByKvubJ44cOdK9e/cP\nPvggPT39hhtuaNOmzZ49e1avXj1+/PjZs2f/3//7f+vVq5eEiQIAULqyw27MmDEffPDB448/\n/thjj9WpUyc+mJ+fP2HChAkTJowbN27SpElVPEkAAMpW9luxb7311lVXXTV+/PhE1UVRVLt2\n7fHjx3fr1u3NN9+syukBAFBeZYfdli1bunbtWuJdl19++ebNmyt7SgAAVETZYdeuXbuNGzeW\neNfGjRtP9jWyAAAkWdlh981vfnPFihVPP/10kfFnn3126dKlvXr1qpqJAQBwaso+eeKnP/3p\n/Pnzv/vd706bNq13796tWrXas2fP8uXL169ff955502cODEJswQAoExlh92ZZ5755z//eezY\nsTNmzHjvvff+/9XS0r71rW+NHTv2zDPPrOIZAgBQLmWHXRRFbdq0+dWvfvX0009//PHHO3fu\nTE9Pb9u2be3atat6cgAAlF8ZYbdz58433njjkksuueaaa2rXrt2hQ4cOHTokZ2YAAJySMk6e\n2Lp163333feLX/wiObMBAKDCygi7Hj16fOMb31i2bNlnn32WnAkBAFAxZYRdnTp1Vq5c2aNH\nj4EDB77++uuffPLJoUOHcv+n5EwUAIDSlX3yRKdOnQoKCj799NOhQ4eWuEAsFqvsWQEAcMrK\nDrvBgwcnYR4AAJymssNu2rRpSZgHAACnqbSwO3r06JYtW3bu3NmxY8d27dqlpKQkbVoAAJyq\nk5488Zvf/CY9Pf2yyy677rrr2rdv37179/fffz+ZMwMA4JSUfMTurbfeuueee6Io6tmz59ln\nn/3OO++8/fbbWVlZGzZsaNSoUXJnCABAuZR8xG7SpElRFL3yyisrVqx4+eWXN23adNNNN33y\nyScvvvhicqcHAEB5lRx2H3zwweWXXz5ixIj4j7Vr1x4/fnwURevXr0/e1AAAOBUlh93u3bs7\nduxYeCT+FbGHDh1KxqQAADh1Jz15Ii0trZQfAQCoacr4SjEAAL4qhB0AQCBO+gbr8uXLEydP\nlD74+9//vvLnBQDAKTpp2G3btm3btm3lGQQAoCYoOezWrVuX5HkAAHCaSg67yy67LMnzAADg\nNDl5AgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDJDru8vLwJEyZkZmY2adIkMzNz/Pjx\neXl55Vz3mWeeadq0aeVuEwAgGMkOuxtvvHH06NH79+8fNmzYZ599NmbMmOHDh5dnxcOHDz/9\n9NOVu00AgJCc9CvFqsLSpUvnz5+flZU1d+7c1NTU48ePDx48eOHChcuWLevdu/fJ1vrjH/+4\nbt26GTNmbNq06cwzz6yUbQIAhCepR+ymTp0aRdHkyZNTU1OjKEpLS5s0aVIURdOnTy9lraFD\nhz7yyCObNm2qxG0CAIQnqWG3bNmyjIyMiy++ODHStWvX9PT0JUuWlLLWwYMHjx49evTo0Ysu\nuqiytgkAEJ7kvRVbUFCwZ8+eHj16FBnPyMhYs2ZNLBZLSUkpccW6devGb9SqVTRDK7zNhPz8\n/Jdeeuno0aOlLPPhhx+WvhEAgJogeWG3d+/eEydONGvWrMh48+bN8/Pz9+/f37x58+Rvc/fu\n3ZMmTTp27Fgpy8SzLxaLner0AACSKXlhFw+jkx1CKz2tqm6bGRkZGzduLH2ZVatWZWZmlnnw\nDwCgeiXvM3YtW7ZMTU09cOBAkfH9+/enpqa2atWqhmwTAOArKnlhV6tWrZYtW27fvr3I+M6d\nO9u0aVP883PVtU0AgK+opKZPr169cnJysrOzEyMbN27ctm1bZmZmjdomAMBXUVLDbuTIkVEU\nTZgwITEyceLEKIpGjRoV/zE/P3/fvn0HDx6sxG0CAHxNJPWbJ/r27Ttw4MCZM2fu2LGje/fu\nK1euXLp0aVZWVuIrIpYvX96/f/8uXbqsXbu2srYJAPA1kdQjdikpKa+99tqYMWNyc3OnTJly\n9OjRcePGzZ49u6ZtEwDgqyipR+yiKKpXr97YsWPHjh1b4r3XXnttKZeL27BhQwW2CQDwNeG8\nUQCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBA\nCDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCA\nQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsA\ngEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7\nAIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAI\nOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBA\nCDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCA\nQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsA\ngEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7\nAIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBAJDvs8vLy\nJkyYkJmZ2aRJk8zMzPHjx+fl5Z3mKhkZGSnFPP7441X5OAAAapy0JP++G2+8cf78+Z06dRo2\nbNjq1avHjBmzevXqBQsWVHiVI0eO7NixIz09vWPHjoXXateuXRU+DACAmiepYbd06dL58+dn\nZWXNnTs3NTX1+PHjgwcPXrhw4bJly3r37l2xVbKzs2Ox2KhRox577LFkPhYAgJomqW/FTp06\nNYqiyZMnp6amRlGUlpY2adKkKIqmT59e4VW2bt0aRVGnTp2qfPYAADVbUo/YLVu2LCMj4+KL\nL06MdO3aNT09fcmSJRVeJR5255133qxZs7Zu3Xr22Wf36NGj8PIAAF8TyQu7goKCPXv29OjR\no8h4RkbGmjVrYrFYSkpKBVaJh11WVtbevXvj96akpIwcOfKpp56qXbt21TwUAICaKHlht3fv\n3hMnTjRr1qzIePPmzfPz8/fv39+8efMKrLJly5Yoinr37v3444+3a9du/fr1Dz744LPPPnvO\nOec8+uijZc5q165dN99885EjR0pZ5ssvv4yiKBaLlbk1AIBqlLywi4dR8cNycceOHavYKqNH\nj87Pzx84cGB8sZ49ey5YsKBjx46TJk368Y9/XKtWGR8ibNKkyfDhw/Pz80tZ5pNPPtm8efPJ\npgEAUEMkL+xatmyZmpp64MCBIuP79+9PTU1t1apVxVbp379/kXtbtGjRr1+/2bNnZ2dnF7kG\nSnFnnHHGgw8+WPoyq1ateuaZZ0pfBgCg2iXvrNhatWq1bNly+/btRcZ37tzZpk2bEg+tVWCV\nuBYtWkRRdPz48dOeNQDAV0ZSL3fSq1evnJyc7OzsxMjGjRu3bduWmZlZsVWys7PbtGlz//33\nF1lrw4YNderUKfNwHQBASJIadiNHjoyiaMKECYmRiRMnRlE0atSo+I/5+fn79u07ePBgOVe5\n4IILzjrrrGnTpq1evTqxwAsvvLBq1apbb701LS3Z36sBAFCNkpo+ffv2HThw4MyZM3fs2NG9\ne/eVK1cuXbo0Kysr8bUTy5cv79+/f5cuXdauXVvOVaZNm9anT59evXpdf/31rVu3/utf/7pi\nxYqOHTs++eSTyXxoAADVLqlH7FJSUl577bUxY8bk5uZOmTLl6NGj48aNmz179ums0q1bt1Wr\nVg0ZMuSdd955/vnnc3Nzf/KTn6xbt65p06ZV/4AAAGqQZL9ZWa9evbFjx44dO7bEe6+99tri\nl4srfZUoirp27Vp6HQIAfB0k9YgdAABVR9gBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABCLZYZeXlzdhwoTMzMwmTZpkZmaOHz8+Ly/vNFepwDYBAMKT\n7LC78cYbR48evX///mHDhn322WdjxowZPnz4aa5SgW0CAIQnLZm/bOnSpfPnz8/Kypo7d25q\naurx48cHDx68cOHCZcuW9e7du2KrVGCbAABBSuoRu6lTp0ZRNHny5NTU1CiK0tLSJk2aFEXR\n9OnTK7xKBbYJABCkpIbdsmXLMjIyLr744sRI165d09PTlyxZUuFVKrBNAIAgJe+t2IKCgj17\n9vTo0aPIeEZGxpo1a2KxWEpKyqmuEovFTnWbxW3btu348eOlLLBz584yN3KKDkVRTmVv86tr\nR3VPoGY6YCcp5NPqnkDN9KmdpJAD1T2BmmlHFJ1Z3XOoOQ5FUaPqnkOVS17Y7d2798SJE82a\nNSsy3rx58/z8/P379zdv3vxUVzl+/PipbrOIDz/8sEOHDrFYrPTFUlJSatWqnKObjRs3jqLn\nomh2pWwtDPXq1atTp051z6IGady4cRQ9GUVPVvdEapDGjTtU9xRqlsaNG+/Zc38U3V/dE6lB\nGje+rrqnUIPUqVOnXr16R48Oqe6J1CyNG4f/J5O8sIvH08kOoR07dqwCq8TvOqVtFtG+ffuD\nBw+eOHGi9MUKCgrS0irnuXryySfHjh1bKZsKRvx/gKp7FjXInDlzcnNzq3sWNYs9pIj169cf\nPXq0umdRszRo0KC6p1CD1KtX77PPPivPv4NfK40aOWJXeVq2bJmamnrgQNGj5fv3709NTW3V\nqlXFVjnVbRbXuHHj8j6GypCWlta0adNk/ka+curUqeMQJqWrX79+/fr1q3sW1GgNGjQQu19D\nyQu7WrVqtWzZcvv27UXGd+7c2aZNmxLf6CzPKqe6TQCAUCU1fXr16pWTk5OdnZ0Y2bhx47Zt\n2zIzMyu8SgW2CQAQpKSG3ciRI6MomjBhQmJk4sSJURSNGjUq/mN+fv6+ffsOHjxY/lXKXAAA\n4GsipcwTQitRLBYbNGjQH/7wh2uvvbZ79+4rV65cunRpVlbWvHnz4gssXry4f//+Xbp0Wbt2\nbTlXKXMBAICviaQesUtJSXnttdfGjBmTm5s7ZcqUo0ePjhs3bvbs0i78UeYqFdgmAECQknrE\nDgCAquO8UQCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCA\nQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsA\ngEAIOwCAQAg7AIBACDsAgEAIOwCAQAi7r7Xc3Nyrr776yiuv/PLLL6t7LtRQdhLKZCehTHaS\npBF2X1+xWOyOO+7Ytm3b9u3bb7/99lgsVt0zosaxk1AmOwllspMkk7D7+hozZsz8+fNfe+21\n1157beHChaNHj67uGVHj2Ekok52EMtlJkirG19Lvfve7lJSU5557Lv7jc889l5KS8vLLL1fv\nrKhR7CSUyU5CmewkSSbsvo7efffdM84446GHHio8+MMf/rB+/frvvvtudc2KGsVOQpnsJJTJ\nTpJ8KTFvdX/N7N69+6qrrrrkkkvmzZtXq9b/ey++oKBg6NCh69ate+f/a+8OWqLswjAAn9ex\njHaVaEj6A9q2KhQqFykUJW0Kopb9jSAI2rtq3TJwJ7VQdFGbghalBUEEFUWRuqpByvkWLb7A\n4gzxfXPeed7rWuoMPIvbx9vjzJzHjw8fPlxwQooTErKEhCwhKaJ148aN0jPQU7dv396zZ8/d\nu3f37dv369erqjp37tyTJ0/evHlz6tSpUuNRB0JClpCQJSRFOLEDAAjCu2IBAIJQ7Bqq0+l8\n+fLlw4cPOzs7pWcB+pVNAnWj2DXL6urqlStXjhw5MjQ0NDw8PDY2tnfv3vHx8UuXLq2urpae\nDugPNgnUltfYNUW73Z6bm7t//35KaWxsbHx8/NChQymljY2N9+/fv3372m/knwAAA8xJREFU\nNqV09uzZe/fuDQ0NFZ4VqCubBOqu6Iet0Ds/P+l7Zmbm6dOnu7+7trZ2+fLllNLNmzd7PxvQ\nL2wSqDkndk1x/Pjxra2tZ8+eDQ4O/vYBnU7n5MmT379/f/jwYY9noyYOHDjQ5SM3Nzf/10mo\nLZuELJukrN//ZBLP+vr63Nzcn3ZxSqmqqsnJyfn5+V5ORa3cunVrfn5+fX09pXT06NFfP1AU\nfrJJyLJJynJi1xQnTpz4+Xd2q9X602Omp6e/ffv26NGjXg5GrXz9+vXYsWMvX75st9teI8Vu\nNgndsEkK0qOb4syZMy9evDh//vzz5893f/fVq1dXr15dXl6emZnp/WzUx/79+69du1Z6CurL\nJqEbNklBTuyaot1uX7x4cXFxMaU0MTExMTFx8ODBqqo2NzffvXv3+vXrlNLs7OzCwoK/rhru\nwYMHFy5c2NrakgR2s0nokk1SimLXLCsrK3fu3FlZWfn06dOPHz9SSq1Wa2RkZGpq6vr166dP\nny49INAHbBKoLcWuoXZ2dj5//tzpdEZGRryyFfg7NgnUjXfFNlRVVYODg9vb26UHob46nc7G\nxsb29vbo6Kjf2fzWwMDA6Oho6SmAf1nWzeIiILKEBKB/+VdsU7gIiCwhAeh7hW68oNdcBESW\nkAD0Oyd2TeEiILKEhCy3RZElJGV580RTuAiILCEhy21RZAlJWU7smsJFQGQJCd1wWxRZQlKQ\nHt0ULgIiS0johtuiyBKSgpzYNYWLgMgSErrktiiyhKQUxa5ZXARElpAA9C/FrqFcBESWkAD0\nHcUOACAIH3fSCEtLS3/3xOnp6f92EmpLSMgSErKEpDgndo1QVdXfPVE8mkNIyBISsoSkOCd2\njfDx48fSI1B3QkKWkJAlJMU5sQMACMI73QAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ\n7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACC\nUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAA\nglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwA\nAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDs\nAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACCUOwAAIJQ7AAAglDsAACC+Aeq/qjz\nYHdzcAAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Absolute Value of Amplitudes”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 5\n",
"[1] \"2.78e-17|000> + -2.78e-17|001> + 2.78e-17|010> + -2.78e-17|011> + 0.707|100> + -0.707|101> + -2.78e-17|110> + 2.78e-17|111>\"\n",
"[1] \"0.354|000> + -0.354|001> + 0.354|010> + -0.354|011> + -0.354|100> + 0.354|101> + 0.354|110> + -0.354|111>\"\n"
]
},
{
"data": {
"image/png": 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Drm3btitXrizzUytXrjzQ\nn5EFAKCaVRx2F1xwwcsvv3z33XeXWL/33nsXLVrUq1evqhkMAICDU/GbJ37961/PnTv3Jz/5\nyf3339+7d++WLVtu2bJl8eLFy5cvP/HEEydMmFANUwIAUKGKw65JkyavvfbamDFjHnrooXff\nfff/3y09/Uc/+tGYMWOaNGlSxRMCAFApFYddFEWtW7e+77777r777o8++mjjxo0ZGRlt2rSp\nXbt2VQ8HAEDlVRB2GzdufPbZZ88666wePXrUrl27ffv27du3r57JAAA4KBW8eeKDDz644YYb\n/vCHP1TPNAAAHLIKwq579+5nnHFGTk7OZ599Vj0DAQBwaCoIuzp16ixZsqR79+4DBw585pln\nPv744507d+76d9UzKAAA5av4zROnnXZaUVHRp59+eskll5S5QTweP9JTAQBw0CoOu0GDBlXD\nHAAAHKaKw+7++++vhjkAADhM5YXdnj171qxZs3HjxlNOOaVt27axWKzaxgIA4GAd8M0Tf/nL\nXzIyMs4555wLL7ywXbt23bp1W7FiRXVOBgDAQSn7iN1LL730gx/8IIqinj17HnfccW+99dab\nb76ZnZ393nvvNWzYsHonBACgUso+Yjdx4sQoip588smXX375iSeeWLVq1WWXXfbxxx8/9thj\n1TseAACVVXbYvf/++507dx4+fHjiw9q1a48bNy6KouXLl1ffaAAAHIyyw27z5s2nnHJK8ZXE\nn4jduXNndQwFAMDBO+CbJ9LT08v5EACAVFPBnxQDAODrQtgBAATigE+wLl68OPnmifIX//73\nvx/5uQAAOEgHDLu8vLy8vLzKLAIAkArKDrt33nmnmucAAOAwlR1255xzTjXPAQDAYfLmCQCA\nQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgECkXNgVFBSMHz8+KyurcePGWVlZ48aNKygoqPzu\njzzySCwWmzt3btVNCACQmlIu7IYNGzZq1Kj8/PwhQ4Z89tlno0ePHjp0aCX3Xb169U033VSl\n4wEApKwD/kmxGrFo0aK5c+dmZ2fPnj07LS1t3759gwYNmjdvXk5OTu/evcvfd8+ePd/97nd3\n7dpVPaMCAKSa1DpiN3Xq1CiKJk2alJaWFkVRenr6xIkToyh64IEHKtz3lltu+eCDD66++uqq\nHhIAIDWl1hG7nJyczMzMM888M7nSqVOnjIyMhQsXlr/jzJkz77nnngcffHDr1q1VPCMAQIpK\nobArKirasmVL9+7dS6xnZmYuXbo0Ho/HYrEyd/zoo49++MMffu9737vuuusmT558UF+0sLDw\n8ccf37NnTznbfPjhhwd1nQAANSKFwm7r1q379+9v2rRpifVmzZoVFhbm5+c3a9as9F6FhYXf\n+973mjZtet999x3CF928efPEiRP37t1bzjaJ7IvH44dw/QAA1SaFwi5RTgc6LHeg9rrrrruW\nLl36yiuvNGrU6BC+aGZm5sqVK8vf5tVXX83KyjrQYAAAKSKFwq5FixZpaWnbt28vsZ6fn5+W\nltayZcvSu/zjH//43e9+N3ny5C5dulTLjAAAqSuF3hVbq1atFi1arF+/vsT6xo0bW7duXatW\nGaMuW7YsHo/ffvvtsX+58847oygaNGhQLBZ78MEHq2NuAIDUkEJH7KIo6tWr15NPPrl27dqT\nTz45sbJy5cq8vLzvfve7ZW5/zjnn3HDDDcVXli1b9sYbb1x44YUnnnjiaaedVuUTAwCkjNQK\nu5EjRz755JPjx49/5JFHEisTJkyIoujGG29MfFhYWPjFF1+kpaU1adIkiqL+/fv379+/+DVM\nnjz5jTfeuOmmm7Kzs6t3dgCAGpZaYde3b9+BAwdOmzZtw4YN3bp1W7JkyaJFi7Kzs5N/dmLx\n4sX9+/fv2LHjsmXLanZUAIBUk0KvsYuiKBaLzZo1a/To0bt27ZoyZcqePXvGjh07c+bMmp4L\nAOBrIOb0bBVKnO6koKCgTp06NT0LQBRFUatWrbZs+VMUlf3642+kX2dlzXvllVdqegyoYal1\nxA4AgEMm7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAA\nAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewA\nAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHs\nAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh\n7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAAC\nIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAA\nAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewA\nAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHs\nAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh\n7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAApFyYVdQ\nUDB+/PisrKzGjRtnZWWNGzeuoKCg/F0+//zzX/ziF2efffbRRx99yimnXH311R999FG1DAsA\nkEJSLuyGDRs2atSo/Pz8IUOGfPbZZ6NHjx46dGg52+/evbtz585/+MMfGjRocNVVV7Vt2/av\nf/3r6aef/vbbb1fbzAAAqSC9pgf4N4sWLZo7d252dvbs2bPT0tL27ds3aNCgefPm5eTk9O7d\nu8xdJk+enJube/vtt0+ePDmxMnfu3MGDB1977bXvvvtuNc4OAFDDUuuI3dSpU6MomjRpUlpa\nWhRF6enpEydOjKLogQceONAuL774Yt26dUePHp1cyc7O7tev33vvvffpp59W/cgAAKkitcIu\nJycnMzPzzDPPTK506tQpIyNj4cKFB9pl9+7dffr0Oeqoo4ov1qlTJ4qi7du3V92oAACpJoWe\nii0qKtqyZUv37t1LrGdmZi5dujQej8disdJ7vfPOOyVWtmzZsmDBghYtWrRr166qZgUASD0p\nFHZbt27dv39/06ZNS6w3a9assLAwPz+/WbNmFV7J6tWrL7roooKCgt/85jfp6RXfuk2bNl1+\n+eVfffVVOdt8+eWXURTF4/EKrw0AoAalUNglyqnMw3JRFO3du7f83b/44otJkyb98Y9/3L9/\n///5P//nBz/4QWW+aOPGjYcOHVpYWFjONh9//PHq1asPNBgAQIpIobBr0aJFWlpa6RfG5efn\np6WltWzZspx9n3nmmRtvvHHjxo0XXXTRb3/729NPP72SX/Soo4665ZZbyt/m1Vdfveeeeyp5\nhQAANSWF3jxRq1atFi1arF+/vsT6xo0bW7duXavWAUf95S9/eckll9SrVy9xtpTKVx0AQEhS\nKOyiKOrVq1dubu7atWuTKytXrszLy8vKyjrQLo888sivf/3rIUOGLFu27EDnugMA+CZIrbAb\nOXJkFEXjx49PrkyYMCGKohtvvDHxYWFh4bZt23bs2JH4MB6PT5w4sWHDhg899FCjRo2qfV4A\ngBSSQq+xi6Kob9++AwcOnDZt2oYNG7p167ZkyZJFixZlZ2cnD8UtXry4f//+HTt2XLZsWfSv\ntzU0a9Zs+PDhpa/t8ccfb968ebXeAACAmpNaYReLxWbNmjVp0qT58+dPmTLl9NNPHzt27B13\n3HGg7XNzc6Mo2rZt20svvVT6swUFBVU4KwBAikmtsIuiqF69emPGjBkzZkyZn/3Wt75V/Hxy\n/fr1c3o5AICE1HqNHQAAh0zYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAAQi5cKuoKBg/PjxWVlZjRs3zsrKGjduXEFBwRHfBQAgPCkXdsOGDRs1alR+\nfv6QIUM+++yz0aNHDx069IjvAgAQnvSaHuDfLFq0aO7cudnZ2bNnz05LS9u3b9+gQYPmzZuX\nk5PTu3fvI7ULAECQUuuI3dSpU6MomjRpUlpaWhRF6enpEydOjKLogQceOIK7AAAEKbXCLicn\nJzMz88wzz0yudOrUKSMjY+HChUdwFwCAIKXQU7FFRUVbtmzp3r17ifXMzMylS5fG4/FYLHb4\nu5SWl5e3b9++cjbYuHFjJcavrN27d2/evPkIXmEAjjrqqFatWtX0FCnk888/37ZtW01PkVoa\nN27crFmzmp4i1XwaRbk1PUPq2F7TA6SczZs37969u6anSC2tWrU66qijanqKqpVCYbd169b9\n+/c3bdq0xHqzZs0KCwvz8/NL/7N+CLuU8OGHH7Zv3z4ej5e/WSwWq1XryBzdHDdu3OTJk4/I\nVQXj6KOP3rFjR+LJdKIouu6665566qmaniK1nH322cuXL6/pKVJIo0aNtmz5aRT9tKYHSSGN\nGl1Y0yOkkP3797dv3/7LL7+s6UFSyx133DFp0qSanqJqpVDYJerqQMfY9u7de0R2KaFdu3Y7\nduzYv39/+ZsVFRWlpx+Z79WECRPuuOOOI3JVwahTp46qK+7xxx/ftWtXTU+RWurVq1fTI6SW\n5cuX79mzp6anSC0NGjSo6RFSSFpa2ubNmyvze/AbpWHDhjU9QpVLobBr0aJFWlra9u0lD6fn\n5+enpaW1bNnyiOxSWqNGjQ5t4EOTnp5+zDHHVOdX5GunTp06derUqekpSGn169evX79+TU9B\nSmvQoIHY/QZKoTdP1KpVq0WLFuvXry+xvnHjxtatW5f5TOgh7AIAEKrUSp9evXrl5uauXbs2\nubJy5cq8vLysrKwjuAsAQJBSK+xGjhwZRdH48eOTKxMmTIii6MYbb0x8WFhYuG3bth07dlR+\nFwCAb4hYhW8IrU7xePyiiy56/vnnv/Wtb3Xr1m3JkiWLFi3Kzs6eM2dOYoMFCxb079+/Y8eO\ny5Ytq+QuAADfEKl1xC4Wi82aNWv06NG7du2aMmXKnj17xo4dO3PmzCO7CwBAkFLriB0AAIcs\ntY7YAQBwyIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQd\nAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCE\nHQBAIIQdAEAghB0AQCCEHQBAIITdN9quXbu6dOly3nnnffnllzU9CynKg4QKeZBQIQ+SaiPs\nvrni8fjVV1+dl5e3fv36q666Kh6P1/REpBwPEirkQUKFPEiqk7D75ho9evTcuXNnzZo1a9as\nefPmjRo1qqYnIuV4kFAhDxIq5EFSreJ8I/3tb3+LxWIPP/xw4sOHH344Fos98cQTNTsVKcWD\nhAp5kFAhD5JqJuy+id5+++2jjjrq1ltvLb5422231a9f/+23366pqUgpHiRUyIOECnmQVL9Y\n3FPd3zCbN28+//zzzzrrrDlz5tSq9f+eiy8qKrrkkkveeeedt956q1WrVjU4ITXOg4QKeZBQ\nIQ+SGpE2ZsyYmp6BajV58uTatWv/9a9/rVevXvH1WCx28cUX/+///u9HH33Ut2/fmhqPVOBB\nQoU8SKiQB0mNcMQOACAQ3hULABAIYfcNFY/Ht23btmnTpqKiopqeBfi68i8JpBph982Sk5Mz\nYsSI448/vm7dus2bN8/IyKhTp05mZub3vve9nJycmp4O+HrwLwmkLK+x+6bYs2fP0KFDn3/+\n+SiKMjIyMjMzmzVrFkVRfn7+hg0bPvnkkyiKBg0aNGPGjLp169bwrECq8i8JpLoaPdkK1Sdx\npu+BAwcuW7as9GdXrFhxxRVXRFE0fvz46p8N+LrwLwmkOEfsvim6d+++Y8eO9957Lz09vcwN\n4vF4nz599u3bt2TJkmqejRRxzDHHVHLL7du3V+kkpCz/klAh/5LUrLJ/MgnP+++/P3To0AP9\nWxxFUSwW69mz5913312dU5FSfvOb39x9993vv/9+FEWnn3568ROKQoJ/SaiQf0lqliN23xQ9\nevRI/H/2/9feHevC1oVxHN7bqJSKmW5uQq0xBSoSPaV7chM6iYJM5QokJBKVQkhQMZmEOeVX\n+E7WRE7smf96npZJVvFm+dlmvL1e72/fMxqNPj4+rq6ufvNgLJT39/eNjY3b29vJZOI9Unzn\nJmEebpIO6ehabG9v39zc7O3tXV9ff//q3d3d4eHh5eXlzs7O75+NxbG2tnZ0dNT1KVhcbhLm\n4SbpkCd2tZhMJgcHB2dnZ03TDIfD4XC4vr7etu3r6+vDw8P9/X3TNLu7u6enp367qtz5+fn+\n/v7b25tJ4Ds3CXNyk3RF2NVlPB6fnJyMx+Onp6fPz8+maXq9Xr/f39zcPD4+3tra6vqAwBJw\nk8DCEnaV+vr6en5+ns1m/X7fO1uBn3GTwKLxqdhKtW27uro6nU67PgiLazabvby8TKfTwWDg\nZzb/a2VlZTAYdH0K4D8u67pYBESRIQFYXv4UWwuLgCgyJABLr6ONF/w2hmSeMwAAAdxJREFU\ni4AoMiQAy84Tu1pYBESRIaHItiiKDEm3fHiiFhYBUWRIKLItiiJD0i1P7GphERBFhoR52BZF\nkSHpkI6uhUVAFBkS5mFbFEWGpEOe2NXCIiCKDAlzsi2KIkPSFWFXF4uAKDIkAMtL2FXKIiCK\nDAnA0hF2AAAh/LuTKlxcXPzshaPR6N+ehIVlSCgyJBQZks55YleFtm1/9kLjUQ9DQpEhociQ\ndM4Tuyo8Pj52fQQWnSGhyJBQZEg654kdAEAIn3QDAAgh7AAAQgg7AIAQwg4AIISwAwAIIewA\nAEIIOwCAEMIOACCEsAMACCHsAABCCDsAgBDCDgAghLADAAgh7AAAQgg7AIAQwg4AIISwAwAI\nIewAAEIIOwCAEMIOACCEsAMACCHsAABCCDsAgBDCDgAghLADAAgh7AAAQgg7AIAQwg4AIISw\nAwAIIewAAEIIOwCAEMIOACCEsAMACCHsAABCCDsAgBDCDgAghLADAAgh7AAAQgg7AIAQwg4A\nIISwAwAIIewAAEIIOwCAEMIOACCEsAMACCHsAABCCDsAgBDCDgAghLADAAgh7AAAQgg7AIAQ\nwg4AIISwAwAIIewAAEIIOwCAEMIOACCEsAMACCHsAABCCDsAgBB/AF3ZBT+sTW9mAAAAAElF\nTkSuQmCC",
"text/plain": [
"Plot with title “Absolute Value of Amplitudes”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 6\n",
"[1] \"0.354|000> + -0.354|001> + 0.354|010> + -0.354|011> + 0.354|100> + -0.354|101> + 0.354|110> + -0.354|111>\"\n",
"[1] \"0.354|000> + -0.354|001> + 0.354|010> + -0.354|011> + 0.354|100> + -0.354|101> + 0.354|110> + -0.354|111>\"\n"
]
},
{
"data": {
"image/png": 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MiRUpY5dOhQmRMDAKh2yQu7WCwWRdHJDqEdO3as9NW/+OKLyZMn//u///uJEyf+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\nYHdzcAAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Absolute Value of Amplitudes”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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MiRUpY5dOhQmRMDAKh2yQu7WCwWRdHJDqEdO3as9NW/+OKLyZMn//u///uJEyf+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\nYHdzcAAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Absolute Value of Amplitudes”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"for (i in 1:6) {\n",
" print(i)\n",
" psi <- O %*% psi\n",
" print(dirac(psi))\n",
" psi <- tensor(G, I()) %*% psi\n",
" print(dirac(psi))\n",
" plotprobs(reduceMeasure(psi, 2, l2r=TRUE)[[1]])\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "muslim-orchestra",
"metadata": {},
"source": [
"From equation 6.14 in Nielsen and Chuang's textbook, we can find $\\theta$ from \n",
"$$M=1$$ and \n",
"$$N=2^n=4:$$\n",
"$$\\theta=\\sin^{-1}\\left(\\frac{2\\sqrt{M(N-M)}}{N}\\right)=\\sin^{-1}\\left(\\frac{2\\sqrt{3}}{4}\\right)=\\frac{\\pi}{3}.$$\n",
"So we start at $\\theta/2=\\pi/6$ and rotate $\\pi/3$ each Grover iteration. So it makes sense that we get the right answer after the first iteration because $\\pi/6+\\pi/3=\\pi/2$ which rotates to the correct orientation in the search basis! Then another 3 rotations is equal to $3*\\pi/3=\\pi$ rotation which is an inconsequential global phase shift; it only swaps the signs of the amplitudes of the two qubits and does not change the probabilities of measurement. So every 3 rotations will periodically result in a successful search. That is why we have a successful search after iteration 1 and iteration 4. After iteration 7, 10, 13, etc. would also be successful."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.4.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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